For a large-scale multi-region AC/DC interconnected power grid with multiple dispatching centers, the distributed solution to optimal power flow calculation is more in line with the information privacy and security requirements. An AC/DC interconnected power grid distributed OPF model is established by duplicating the tie-lines into adjacent regions and introducing boundary consistency constraints, and a fully distributed algorithm called Synchronous Alternating Direction Method of Multipliers (SADMM) with no form of central controllers is proposed. With regard to network partitioning for DC tie-lines, convertor stations are maintained in their own regions and only the DC transmission lines are duplicated. The proposed SADMM is improved based on the Gauss-Seidel ADMM (GS-ADMM), by using the weighted average value of boundary variables of adjacent regions obtained from current iteration as the reference values of both regions for the next iteration, which realizes the parallel computation among different regions. Moreover, the value of penalty factor is rationally determined based on the characteristics of the optimal problem, and the convergence speed is accelerated. The algorithm is tested with an actual AC/DC interconnected power grid and two modified IEEE AC/DC systems, and by comparing with the results obtained from centralized algorithm, its correctness and effectiveness can be validated. This work is supported by National Key Basic Research Program of China (973 Program) (No. 2013CB228205) and Natural Science Foundation of Guangdong Province (No. 2015A030313233).